(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Inexpensive global location and tracking systems using geostationary satellites."

NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 



INEXPENSIVE GLOBAL 
LOCATION AND TRACKING SYSTEMS 
USING GEOSTATIONARY SATELLITES 



Danny L. DeFries 
June 1989 



Thesis Advisor 



Tri T. Ha 



Approved for public release; distribution is unlimited. 



P4406A 



[^classified 



sification of this paG 



REPORT DOCUMENTATION PAGE 



Report Security C!a 



i Unclassified 



y Classification Authont 



Declassification Downgrading Schedule 



Performing Organization Report N'umber(s) 



3 Distribution Availability of Report 

Approved for public release; distribution is unlimited. 



g Organization Report Number(s) 



i Name of Performing Organizat 
i.'aval Postgraduate School 



6b Office Symbol 
( if applicable) 62 



7a Name of Monitoring Organizati 
Naval Postgraduate School 



: Address (city, state, and ZIP code) 

lonterev, CA 93943-5000 



7b Address (city, state, and ZIP code) 

Monterey, CA 93943-5000 



Name of Funding Sponsoring Organizai 



9 Procurement Instrument Identification Number 



; and ZIP code) 



10 Source of Funding Numbers 



Program Element No | Project No | Task No | Work Unit Accession No 



Title (include secuntv classification) INEXPENSIVE GLOBAL LOCATION AND TRACKING SYSTEMS USING 
EOSTATIONARY SATELLITES 



) Danny L. DeFries 



Ja Type of Report 
Iaster's Thesis 



14 Date of Repoi 
June 1989 



(year, month, day) 



15 Paae Count 
43 



> Supplementary Notation The views expressed in this thesis are those of the author and do not reflect the official policy or po- 
tion of the Department of Defense or the U.S. Government. 



Group 



IS Subject Terms (continue on reverse if necessary and identify by block n 
Geostationary Satellite Navigation, position determination. 



) Abstract (continue on reverse if necessary and identify by block number) 

Inexpensive Global Location and Tracking Systems are currently being designed to provide the civilian market low-cost 
idio position determination. This paper discusses two possible designs. The first design employs 3 or 4 satellites, depending 
n whether altitude is known a priori, each transmitting continuous ranging signals. The user transceiver receives the ranging 
gnals. measures the time differentials of the receipt of the signals and transfers this information to a control station via a 
itellite link. The control station computes the user position from this data and sends the position coordinates back to the 
ser via another satellite link. In the second design, each user transceiver transmits a unique code to the control station via 
le 3 or 4 satellite links, again depending on whether the altitude is known a priori. The control station measures the time 
ifferentials of the receipt of the signals and determines the user position. This position information is then transmitted back 
5 the user via a satellite link. 



Distribution Availability of Abstract 

^ j-.;iassified unlimited D same as report 



21 Abstract Security Classification 

Unclassified 



2a Name of Responsible Individual 
n T. Ha 



22b Telephone (include Area c 
(408) 646-2788 



22c Office Symbol 
62Ha 



D FORM 1473.84 MAR 



security classification of this page 



Approved for public release; distribution is unlimited. 

Inexpensive Global 
Location and Tracking Systems 
Using Geostationary Satellites 

by 

Danny L. De Fries 

Major, United States Army 

B.S., University of South Dakota, 1975 

Submitted in partial fulfillment of the 
requirements for the degree of 

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING 

from the 

NAVAL POSTGRADUATE SCHOOL 

June 1989 



ABSTRACT 

Inexpensive Global Location and Tracking Systems are currently being designed to 
provide the civilian market low-cost radio position determination. This paper discusses 
two possible designs. The first design employs 3 or 4 satellites, depending on whether 
altitude is known a priori, each transmitting continuous ranging signals. The user 
transceiver receives the ranging signals, measures the time differentials of the receipt of 
the signals and transfers this information to a control station via a satellite link. The 
control station computes the user position from this data and sends the position coor- 
dinates back to the user via another satellite link. In the second design, each user 
transceiver transmits a unique code to the control station via the 3 or 4 satellite links, 
again depending on whether the altitude is known a priori. The control station measures 
the time differentials of the receipt of the signals and determines the user position. This 
position information is then transmitted back to the user via a satellite link. 



U'l^ 



TABLE OF CONTENTS 

I. INTRODUCTION 1 

II. SYSTEM I 5 

A. SYSTEM I DESCRIPTION 5 

B. SATELLITE-TO-USER DOWNLINK 5 

1. Downlink Frequency and Bandwidth 5 

2. Pseudo-Noise (PN) Ranging Code 6 

C. USER-TO-CONTROL STATION LINK 7 

1. Uplink Bandwidth 7 

2. User-to-Control Station Data 9 

3. Satellite-to-Control Station Downlink 13 

D. POSITION DETERMINATION 13 

E. POSITION ERROR 19 

F. CONTROL STATION-TO-USER DATA LINK 23 

1. Uplink Bandwidth 23 

2. Control Station-to-User Data 24 

3. Satellite-to-User Downlink 25 

III. SYSTEM II 26 

A. SYSTEM II DESCRIPTION 26 

B. USER-TO-CONTROL STATION LINK 27 

1. Uplink Bandwidth 27 

2. User-to-Control Station Data 27 

3. Satellite-to-Control Station Downlink 28 

C. POSITION DETERMINATION 28 

D. CONTROL STATION-TO-USER DATA LINK 29 

1 . Uplink Bandwidth 29 

2. Control Station-to-User Data 30 

3. Satellite to User Downlink 30 

IV. SYSTEM COMPARISONS AND CONCLUSIONS 32 



V. LIST OF REFERENCES 33 

VI. INITIAL DISTRIBUTION LIST 34 



LIST OF TABLES 

Table 1. SYSTEM I USER-TO-CONTROL STATION LINK ANALYSIS . . 

Table 2. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

Table 3. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

Table 4. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

Table 5. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

Table 6. SYSTEM I CONTROL STATION-TO-USER LINK ANALYSIS . . 

Table 7. SYSTEM II USER-TO-CONTROL STATION LINK ANALYSIS . . 

Table 8. SYSTEM II CONTROL STATION-TO-USER LINK ANALYSIS . . 



10 
14 

15 
16 
17 
24 
28 
31 



LIST OF FIGURES 

Figure 1. Geocentric Coordinate System 2 

Figure 2. Differential Distance Measurement 7 

Figure 3. Data Frame (User to Control Station) 11 

Figure 4. TDM Frame (Control Station to Users) 25 



I. INTRODUCTION 

Today, the United States Department of Defense (DOD) is utilizing the XAVSTAR 
Global Positioning System (GPS) for accurate position determination. GPS employs 18 
geosynchronous satellites within 6 different orbits with 3 satellites in each orbit. GPS 
provides highly accurate position determination to an unlimited number of users world- 
wide, although the position determination accuracy provided to the civilian community 
is intentionally degraded due to national defense reasons. The degraded mode still ena- 
bles the civilian community to attain accuracies of 100 meters. 

In addition to the high number of operational satellites that are required to support 
the 24-hour world-wide GPS system, the user equipment cost is also quite high due to 
its complexity. Even though the user equipment cost has decreased considerably since 
GPS was first introduced, the civilian community can not afford the user equipment. 
To lower the cost of the position determination system so that the civilian community 
can afford to install position determination equipment in one's vehicle, a simpler system 
has to be designed and the total number of satellites deployed has to be reduced. 

This thesis presents two low-cost concepts of vehicle location and tracking using 
geostationary satellites. The first concept is borrowed from the concept of geostationary 
satellite navigation systems presented in [Ref. 1]. The second concept is a new concept 
that is presented in this thesis. For the systems to be utilized by the civilian community, 
the systems have to be lower in cost than GPS, provide reasonable position accuracy, 
and be reliable. To cover the United States, each system requires four satellites to de- 
termine longitude, latitude, and altitude, or three satellites if altitude is not measured. 
Like the geostationary satellite navigation system, the location and tracking systems will 
also deploy three or four geostationary satellites parked in orbits on the equator at a 
latitude of zero degrees and altitude of approximately 35,786 kilometers. The difference 
between the proposed location and tracking system and the geostationary navigation 
system is that the location and tracking system user does not determine his position but 
relies on the central control station to determine it. The satellites continuously and 
synchronously transmit a satellite-unique ranging code to the user on earth. The user 
receives the satellites signals at different times due to the path length differences between 
the user and each of the satellites. The transceiver measures the time differentials be- 
tween a designated signal and the remaining signals and transmits this information to a 



control station via a satellite communications link. The control station calculates the 
user position from the time differentials and transmits the user coordinates to the user 
via another satellite channel. By placing the computational burden on the central con- 
trol station, the location and tracking transceiver can be made at a lower cost. 

Position determination in a geostationary coordinate system is normally defined in 
a geocentric coordinate system as shown in Figure 1. The x-axis is the intersection of 
the equator plane (0° latitude) and the Greenwich meridian plane (0' longitude) and is 
oriented from the center of the earth, the z-axis is the polar axis oriented from south to 
north, and the y-axis completes the right-handed Cartesian coordinate system. We des- 
ignate the unknown user position by (x,y,z), the known positions of n = 3 or 4 
geostationary satellites by (x t ,y n z,) where /= 1, 2, ..., n, and the known position of the 
central control station by (.r ..)'o, z ). 



O'Longiludo 




Figure 1. Geocentric Coordinate System: (Ref. 1] 



The main function of the transceiver is to measure the differential distance 

fl . = d x -d b i= 1,2,..., n (1) 

representing the differences in the distance to the user from one satellite, arbitrarily- 
designated as satellite one, and from each of the other satellites. The variable a, repres- 
ents the difference in the distance of satellite one to the user and that of each of the other 
satellites to the user. The variable d, represents the distance from each satellite to the 
user. The differential distance determination concept is discussed later. The squared 
distance from the user position to each geostationary satellite can be expressed by 

4 = (x - a--) 2 + (y -yf + (z - zf, f=l,2, ..., n (2) 

where (x,y, z) represent the users coordinate position in the Cartesian coordinate system 
and {x t ,y,. z,) represents each of the satellites' positions. 

For n = 4. (1) and (2) combine to form a set of four independent equations and four 
unknowns, namely, x, y. z, and d x . These four equations are 

(rf, - af = (x - xf + Cv -})) 2 + (z - z t ) 2 , 1=1,2, ..., 4 (3) 

which can be solved using the measured data a, and the known satellite ephemeris 
(x,.y,. z), i = 1. 2. 3, 4. The value a, is found through the use of a correlation register and 
ranging codes which will be discussed later. A detailed discussion of the concept can be 
found in[Ref. I]. 

For the three satellite system, n = 3, we use 

. v 2 + / + 2 2 = (£ + /*) 2 (4) 

where R = 6378 km is the Earth's mean equatorial radius, and h is the user altitude 
(assumed to be known), as the fourth equation in addition to the three equations 

(4 - a y = (x - x,y- + Cv - y,y + (z - z,y- /= 1,2,3. 

The first system requires each satellite to broadcast a unique pseudo-noise (P\) 
code in the frequency band 24S3.5 - 2500 MHz. The PX codes are selected from a set 
of Gold codes which allow minimum interference between signals from various satellites. 
The satellites employ extremely stable on-board atomic clocks which are mutually syn- 
chronized. A central control station which can view all satellites is responsible for the 
clock correction via a communications link in the frequency band 6526.5 - 6541.5 MHz. 
The user transceiver measures the time differentials between one satellite arbitrarily 



designated as satellite one, and each of the other satellites. The accuracy of the meas- 
urements and their effect on the user position determination accuracy will be discussed 
later. The user transceiver then sends the measured time differentials to the central 
control station for computing the user coordinates via a code division multiple access 
(CDMA) uplink in the frequency band 1610 - 1626.5 MHz. The central control station 
calculates the user coordinates using the received time differentials and the predicted 
satellite ephemerides. It then relays the coordinates to the user via a time division mul- 
tiplexed (TDM) downlink in the frequency band 2483.5 - 2500 MHz. 

The second system requires the user transceiver to broadcast a PN code to the cen- 
tral control station via a code division multiple access uplink. The central control sta- 
tion calculates the user differential distances to the satellites with the available satellite 
ephemeris and then the user coordinates which are relayed to the user via the TDM 
downlink. 



II. SYSTEM I 

A. SYSTEM I DESCRIPTION 

The frequency assignment and bandwidth allocated for each of the satellite links 
listed below are assigned by the Federal Communications Commission as listed in [Ref. 
2J. 

• Satellite-to-User Ranging Link 

Frequency 2483.5 - 2493.73 MHz 
Bandwidth 10.23 MHz 

• User-to-Control Station 

User-to-Satellite Uplink 
Frequency 1610 - 1626.5 MHz 
Bandwidth 16.5 MHz 
Satellite-to-Control Station Downlink 
Frequency 5150 - 5166.5 MHz 
Bandwidth 16.5 MHz 

• Control Station-to-User 

Control Stution-to-Satellite Uplink 

Frequency 6524.5 - 6530.77 MHz 
Bandwidth 6.27 MHz 
Satellite- to- User Downlink 
Frequency 2493.73 - 2500 MHz 
Bandwidth 6.27 MHz 

• Control Station-to-Satellite Command Link 

Frequency 6526.5 - 6541.5 MHz 
Bandwidth 15 MHz 

B. SATELLITE-TO-USER DOWNLINK 
I. Downlink Frequency and Bandwidth 

The communications downlink from each of the satellites to the user occupies 
a bandwidth of 16.5 MHz from 2483.5 to 2500 MHz. Within this bandwidth, the satel- 
lites must transmit a pseudo-noise ranging code needed for user position determination 
and provide the downlink for the control station-to-user data link. In System I design, 
the satellites must employ two satellite-to-user channels, one for the sole purpose of 
transmitting the unique pseudo-noise code and one to perform as a relay for the data 
link from the control station to the user. The pseudo-noise code will be transmitted 
between the frequencies of 2483.5 and 2493.73 MHz in a bandwidth of 10.23 MHz. The 
control station-to-user data link will be transmitted between the frequencies of 2493.73 
and 2500 MHz in a bandwidth of 6.27 MHz. 



2. Pseudo-Noise (PN) Ranging Code 

The PN ranging code transmitted by the satellites is received by the user and is 
used to determine time differentials. The accuracy of the measurements of the time dif- 
ferentials used to determine the user position is of prime importance to the overall po- 
sition accuracy. The more precise the time measurement is, the more accurate the 
position determination will be. GPS uses code chip rates of 10.23 Mbit/s in its trans- 
missions to the user. For our example, a given code length of 2 19 - 1 = 524,287 chips 
and a chip rate of 10.23 Mbit/s results in a code period of 524,287, 10.23 x 10 6 = 51.25 
ms. A lower code length of 2 16 —1 = 65,535 and a lower chip rate of 1.023 Mbit/s has a 
period of 65,535 1.023 x 10 6 = 64.06 ms and a larger error in the differential distance 
measurement. The code tracking loop that would be used is able to maintain code 
alignment to approximately 0.01 chip. This is a conservative figure, for code tracking 
loops can be accurate to 0.001 chip. For a 0.01 alignment factor and a 10.23 Mbit/s chip 
rate, a ranging error of 0.29 meter would exist, where a 1.023 Mbit s chip rate would 
have a ranging error of 2.9 meters [Ref. 1]. To better understand the fundamentals of 
PN ranging codes that determine position accuracy, Figure 2 shows the concept of dif- 
ferential distance measurement. To determine the differential distance, the user equip- 
ment must be able to perform a correlation operation among the satellites' codes and 
internally stored copies of those codes. The receiver clock must be able to count the 
number of chips between the correlation peak of the first received code and the subse- 
quent codes as shown in Figure 2. Since a, may not be an integer multiple number of 
chips, the receiver may use the correlation value relative to the peak correlation voltage 
to determine a fraction of a chip in the measurement. As was stated earlier, a fraction 
of a chip of 0.001 can be measured. 



- PN Code Period - 



Figure 2. Differential Distance Measurement: [Ref. 1] 



In [Ref. 1], the PN ranging code and its effects on position determination accuracy is 
discussed in further detail. 

C. USER-TO-CONTROL STATION LINK 
1. Uplink Bandwidth 

The frequency bandwidth allocated to the user-to-control station data link is 
1610-1626.5 MHz. The user direct sequence spreads the data with a Gold code of period 
2 10 - 1 = 1023 chips which is a standard period for navigation systems. Thus for a 
bandwidth of 16.5 MHz from 1610-1626.5 MHz, the typical user data rate is approxi- 
mately 16,129 bits s when spread at 1023 chips per bit, if Quaternary Phase Shift Keying 
(QPSK) is used as a modulation scheme. That is, the chip rate is ( 16, 129)( 1,023) = 
16.5 x 10 6 chips. With QPSK, there are 2 bits per symbol and hence the symbol rate is 
S.5 x 10 6 symbols a second. The bandwidth required (double sideband for QPSK) is 
twice the symbol rate or equal to 16.5 MHz which is compatible with the available 16.5 
MHz bandwidth. The users must share this available bandwidth with each other to 
transmit their IDs, time differentials, and other information to the control station. 

The user-to-satellite uplink is the most critical link in the system. The user is 
not able to employ or utilize a high gain dish antenna like those used in the fixed 
stations. The maximum output RF power is also limited by the power available in a 
mobile vehicle. To calculate the Jiffective Isotropic Radiated Power (El RP) of a vehicle, 



Eq. (5) is used, where P, is the transmitter power out and G t is the effective gain of the 
antenna. 

E1RP = P t G t (5) 

In our design, a transmitter power out of 80 watts which is equal to 19 dBW and an 
omni directional antenna with a gain of 4 dB will yield an EIRP of 23 dBW. These design 
values are selected with some judgment and are also being used in current navigation 
systems. 

The Free Space Path Loss (FSPL) is calculated using Eq. (6). 

FSPL(dB) = 10 log( ^- \ (6) 

where/is the carrier frequency, */is the slant range, and c is the speed of light. At a slant 
range of 35.786 km and a carrier frequency of 1618 MHz, a FSPL of approximately 190 
dB is obtained. 

A standard satellite G,'T of + 3 dB K has been chosen for this design model and 
Boltzmann's constant k is given as -228.6 dBW/K-Hz. To calculate the uplink carrier- 
to-noise density ratio, Eq. (7) is used. 

-£■ {dB) = EIRP{dB\\ r ) - FSPL{dB) + y {dbjK) - k{dBW!K-Hz) (7) 

The EIRP of 23 dBW, FSPL of 190 dB, satellite GT of +3 dB K and Boltzmann's 
constant of -228. 6 dBW K-Hz are entered into the Eq. (7), obtaining an uplink carrier- 
to-noise density ratio of 64.6 dB-Hz. This density ratio is sufficient to support the data 
rate that the system requires for successful operation. 

For the downlink, the same calculations are performed to obtain the downlink 
carrier-to-noise density ratio. A FSPL of 198 dB is calculated for the carrier frequency 
of 5150 MHz. A satellite EIRP of 36 dBW and a control station G/T of 20 dB K are 
used to calculate the downlink carrier-to-noise density ratio. These values are standard 
satellite EIRP and station G T values. 

The total carrier-to-noise density ratio is calculated using Eq. (8) found in [Ref. 
3]. 

(#)-[(*):♦(#);] 



To solve for the total carrier-to-noise density ratio, the values of the carrier-to-noise 
density ratios must be converted to real numbers, substituted into Eq. (8), the equation 
solved and the answer converted to the logarithm form of dB-Hz. 

A margin of 2 dB is further engineered into the system design to allow for in- 
terferences that would degrade the operation of the system. The data rate is calculated 
by subtracting the 2 dB margin from the total carrier-to-noise ratio, converting that dB 
value to a factor and then dividing that factor by the equivalence of the required 
signal-to-noise ratio which is set to two representative values of 15 and 20 dB for this 
system design. These required signal-to-noise ratios are typical satellite navigation 
signal-to-noise ratios; each will be used for design calculations. 

To calculate the data rate for a lower required signal-to-noise ratio of 15 dB, the 
2 dB margin is subtracted from the total carrier-to-noise ratio of 64.57 dB-Hz, giving 
62.57 dB-Hz. This ratio is converted to a value of 1.807 x 10 6 and is divided by 31.26 
(value of 15 dB) which in turn yields the data rate of approximately 57 kbps. When the 
required signal-to-noise ratio is increased to 20 dB (factor of 100), the data rate is low- 
ered to IS kbps. The link analysis is tabulated in Table 1. 
2. User-to-Control Station Data 

After receiving 3 or 4 satellites' ranging signals and measuring time differentials, 
the user must transmit the information to the control station for calculation. The 
transmission is Code Division Multiple Access (CDMA) as required by the Federal 
Communications Commission (FCC) and is designed to provide the system with a bit 
error probability of 10" 6 to 10"". (A bit error probability of 10~ 6 and 10"" provides the 
reliability needed for a successful system.) The data stream must include a synchronous 
code word in the user transmission for the control station to synchronize to the trans- 
mission. Once the the control station has synchronized itself to the data transmission. 
the control station can identify the information that the user is sending to the control 
station from within the data frame. A Barker code word of 13 bits would provide the 
synchronization that the control station equipment requires and enable the control sta- 
tion to lock on to the transmission and recover the user transmitted data [Ref. 4]. 

Other information that is sent includes the user ID, the ID of the satellite that 
was received first, the second and third satellites IDs and the time differentials AT in 
symbols between receipt of the signals of the satellites. These time differentials are de- 
termined by the correlator. The minimum distance that a satellite may be from the user 
is 35,786 km which corresponds to a minimum propagation delay of 119.287 ms. The 
maximum distance is 41.678.82 km which corresponds to the maximum propagation 



Table 1. SYSTEM I USER-TO-CONTROL STATION LINK ANALYSIS 



Uplink Frequency 


1618 MHz 


Antenna Gain 


4dB 


Transmitted Power 


80 W 


Carrier EIRP 


23 dBW 


Free Space Path Loss 


190 dB 


Satellite G T 


+ 3 dB K 


Boltzmann's Constant 


-228. 6 dBW K-Hz 


Uplink 

Carrier-to-Noise 

Density Ratio 


64.6 dB-Hz 


Downlink Frequency 


5150 MHz 


Satellite EIRP 


36 dBW 


Free Space Path Loss 


198 dB 


Control Station G T 


20 dB K 


Downlink 

Carrier-to-Noise 

Density Ratio 


86.6 dB-Hz 


Total 
Carrier-to-Noise 

Density Ratio 


64.57 dB-Hz 


Margin 


2dB 


If required -rr- = 


15 dB 


20 dB 


Then Data Rate can be 


57 kbps 


18 kbps 



delay of 138.929 ms. A maximum time differential between the minimum and maximum 
time delays is 19.642 ms. We require an accuracy of 0.1 /j.sec. This allows a quantization 
interval of 0.2 ,usec. The number of 0.2 /isec intervals in 19,642 /isec is 98,210. To rep- 
resent this value, 2 18 = 262,144 will easily suffice to represent the maximum time differ- 
ential. Thus there are 18 bits required to represent the maximum differential time 
measurement between the first satellite and each of the other satellites and 2 additional 
bits to identify the satellite for a total of 20 bits used. In the three-satellite design, the 
altitude of the user must also be transmitted to the control station for position determi- 
nation. An altitude of 100,000 meters with 0.1 meter accuracy can be represented with 



20 bits. For the four-satellite case, the field for altitude is used for satellite 4 ID and 
differential time measurement. In all cases, 20 bits for additional information are de- 
signed into the frame for future uses such as emergency reporting of position location 
when the user may be in need of it. See Figure 2 for an example of a data frame. 



111 BITS 



1 3 


16 


2 


20 




20 




20 


20 


-4 ► 


^ ► 


<« ► 




































ALTITUDE 




SYNC 


USER 
I D 


SAT 1 
I D 


S A T 
1 D & 


2 
D T 


SAT 
I D & 


3 
D T 


SAT 4 
1 & D T 


GENERAL 
INFORMAT ION 



Figure 3. Data Frame (User to Control Station) 



To increase the number of channels that could exist on the system, Forward 
Error Correction (FEC) is used. The use of FEC lowers the required signal-to-noise 
ratio and thus allows more CDMA channels to be used. A convolution code with 
Viterbi decoding and soft decision will increase the total number of channels [Ref. 5]. 
There are various combinations of convolution code rates and constraint lengths that 
can be examined to provide the optimum data rate for the system. 

To calculate the number K + 1 of CDMA channels that can successfully exist 
within the bandwidth at a bit error probability of 10 6 and 10~ 7 , the following results 
from Refs. 5 and 6 were used. To calculate the number K+ 1 of CDMA channels that 
can be succesfully utilized simultaneously, Eq. (9) is used. 



A' =3 A" 



_Ao_ 
2E h 



(9) 



The chips per bit (N), the design bit energy-to-noise ratio I -rr- 1 and the bit energy- 
to-noise plus user interference density ratio ( -— ) must be known to solve for K. For 



reliability, bit energy-to-noise ratios of 15 and 20 dB were selected for the system. The 
chips per bit (N) is 1023. The value for the bit energy-to-noise plus user interference 
density ratio is a function of other parameters as follows. 



/m-S.) 



where Q{x) is defined as 



ew- 



e~du (11) 



The code rate (R) and the channel transition probability (p) must be known to calculate 
the energy-to-noise plus user interference density ratio. A code rate (R) of 1,2 to 7,8 
was used in the calculations to determine the bit rate that will support the maximum 
number of CDMA channels. The probability (p) is a function of parameters that are 
determined by the code rate and system design. To calculate p, Eq. 12 is used [Ref. 6]. 

P b ,code d <-J \J df "'P 2 (12) 

For System 1 design, coded bit error probabilities (P btCCded ) of 10~ 6 and 10" 1 are 
used to insure a reliable system for the user. The number k of encoder input bits and 
the number n of encoder output bits establish the code rate (R), where R = —. The 
variable B d used to calculate the channel transition probability (p) is a calculated value 
that is determined by the code rate, constraint length, and the free distance of the code. 
The variable d fret is the free distance of the convolutional code and is determined by the 
code rate and the constraint length. The values B d and d /r „ have been previously cal- 
culated in [Refs. 5,6] at a constraint length of 7 for the code rates of 1/2 to 7 8. 

To calculate the number of simultaneous CDMA channels that the system can 
support, the channel transition probability (p) must be found with Eq. (12). The number 
k of encoder input bits. B d , d,,„ and the coded bit error probability (P byCOded ) are entered 
into Eq. (12) to solve for the channel transition probability (p). Then the bit energy- 
to-noise plus user interference density ratio ( -~ ) is substituted into Eq. (10) along 
with the given chips per bit (N) of 1023, and the design bit energy-to-noise density 



ratio -rr- J of 15 and 20 dB. In Tables 2 and 4, the number K+ 1 of channels that can 
successfully be used with hard decision Viterbi coding at a bit error probability of 10 -6 
and 10 _ " respectively are shown. For example, given the code rate (R) of 1/2, the en- 
coded bit k is 1, B d is 36, and d fr „ is 10. For a P btCOded of 10~ 6 a channel transition 
probability (p) of .00703 is calculated. With a p of .00703 and a code rate (R) of 1/2, a 
bit energy-to-noise plus user interference density ratio ( -^- \ of 5.87 is calculated. This 
value, the chips per bit (N) of 1023, and the design energy-to-noise density ratio of 20 
dB (100) yields a value K of 246. The number of channels K+ 1 is then 247. An in- 
spection of the tables reveals that a code rate of 1/2 yields the largest number of simul- 
taneous channels that can be used successfully. When soft decision Viterbi coding is 
used, a decrease in the bit energy-to-noise plus user interference density ratio of 2 dB is 
realized. Thus soft decision Viterbi coding further increases the number of CDMA 
channels that can be used which is shown in Tables 3 and 5 for 10 -6 and 10 _ " respectively. 
The different bit error probabilities of 10~ 6 and 10"' and soft and hard Viterbi decisions 
are used in the calculations to provide the reader an indication of four possible system 
capabilities. 

The major limitation in using lower code rates of 1/2 is that the bandwidth of 
the system that is available to the user is severely reduced. Although the number of 
CDMA simultaneous channels is greatly increased, the bandwidth of the system is de- 
creased. Further research is required in the area of the coding techniques to find the 
maximum number of CDMA channels that can be used with the highest coding rate to 
allow for the greatest user bandwidth. 

3. Satellite-to-ControI Station Downlink 

The frequency bandwidth allocated for the satellite-to-control station downlink 
is 16.5 MHz from 5150 to 5165.5 MHz. The satellite serves as a relay for the user-to- 
control station data link. 

D. POSITION DETERMINATION 

After receipt of the time differentials, the central control station computes the co- 
ordinates of the user from the measured time differentials, and the known location of 
each of the satellites. 

The x, y. z position determination of the user is defined in a geocentric coordinate 
system as shown in Figure 1. The x axis is the intersection of the equatorial plane and 
the Greenwich Meridian plane and is oriented from the center of the earth. The y axis 



Table 2. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

(Hard Decision) at Coded Bit Error probability of IP" 6 



Code 

Rate 

R 


1,2 


2/3 


3/4 


4,5 


5/6 


6/7 


7/8 


k 


1 


9 


3 


4 


5 


6 


7 


\ a 


36 


3 


42 


12 


92 


5 


9 


"free 


10 


6 


5 


4 


4 


3 


3 


CDMA Channels K 
for— j-= 100 or 20 dB 


247 


237 


185 


172 


157 


147 


145 


CDMA Channels K 

E h 
for-rf = 32 or 15 dB 


213 


204 


152 


139 


124 


114 


112 



completes the cartesian coordinate system with the x axis. The z axis is the north to 
south axis connecting the two poles. 

Although actual distance is not measured by the user equipment, the distance can 
be calculated from the time it took for the other satellites signals to reach the user versus 
the first satellite signal that was received. The time differentials are converted to differ- 
ential distances by multiplying the time differentials by the speed of light (c); approxi- 
mately 3 x 10 8 m s. The accuracy of the synchronization of the satellites transmissions 
plays an important part in the users position determination. If the satellites do not 
transmit at the exact same time, the time differentials will not be correct and thus neither 
will the distance differentials. 

The distance between the unknown user position (x, y, z) and each of the satellites 
(.v, j/, 2,) where /= 1, 2, . . ., n can be calculated from 



--(x-xf + ^-yf + iz-zf /= 1, 2, 



We further define the distance measurements 

a,= d, — d< i= 1, 2. . . ., n 



(13) 



(14) 



Table 3. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

(Soft Decision) at Coded Bit Error probability of lO 6 



Code 

Rate 

R 


1/2 


2/3 


3,4 


4/5 


5/6 


6/7 


7/8 


k 


1 


2 


3 


4 


5 


6 


7 


**. 


36 


3 


42 


12 


92 


5 


9 


<7>f<? 


10 


6 


5 


4 


4 


3 


3 


CDMA Channels K 
for-^-= 100 or 20 dB 


400 


384 


302 


281 


258 


242 


238 


CDMA Channels K 
for -r^-= 32 or 15 dB 


366 


351 


269 


247 


225 


209 


206 



as the difference in distance from one satellite designated as satellite one to the user and 
the other satellites distance to the user. 

For a four satellite case, n = 4, equations (13) and (14) are combined to form four 
independent equations and four unknowns, x, y, z, and d v From the known satellite 
positions and the time differences which have been measured by the user, the four un- 
knowns can be solved. Sign ambiguities can be corrected as long as the user knows what 
quadrant he is in. 

The coordinates of the satellites (x„ y„ z) can be calculated from its longitude 
eastward of zero degrees bv 



Xi = r cos t 

y) = r sin 6 
z- = Q 



(15) 
(16) 

(IV) 



The term z, will remain zero as the satellites are in an equatorial orbit with a latitude of 
zero degrees. 



Table 4. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

(Hard Decision) at Coded Bit Error probability of 10 _ " 



Code 

Rate 

R 


1/2 


2/3 


3/4 


4/5 


5/6 


6/7 


7/8 


k 


1 


2 


3 


4 


5 


6 


7 


%,. 


36 


3 


42 


12 


92 


5 


9 


dfree 


10 


6 


5 


4 


4 


3 


3 


CDMA Channels K 
for-rr-= 100 or 20 dB 


215 


200 


159 


147 


135 


123 


122 


CDMA Channels K 
for -rr=32 or 15 dB 


181 


167 


126 


112 


102 


89 


88 



The four non-linear independent equations are 

(4 - af = (x - xf + [y -yf + z 2 i - 1, 2, 3, 4 



(18) 



Equation (18) can be reduced to 3 linear independent equations by substituting equation 
(14) into equation (13) and subtracting the (/= 1) equation from the other 3 equations. 
The remaining three equations are 

2 

( Xl -x,)x + tv*,-J-,lv - fl/4 = --j- f — 2, 3, 4. (19) 

The 3 equations can then be entered into matrix form to solve x, y, and d x as shown: 



_x A — x } y 4 — J', — a 4 



(20) 



7 can be calculated by substituting equation (20) into equation (18 



Table 5. NUMBER OF SIMULTANEOUS CDMA CHANNELS WITH FEC 

(Soft Decision) at Coded Bit Error Probability of 10"' 



Code 

Rate 

R 


1/2 


2/3 


3/4 


4/5 


5/6 


6/7 


7/8 


k 


1 


2 


3 


4 


5 


6 


7 


\„ 


36 


3 


42 


12 


92 


5 


9 


"free 


10 


6 


5 


4 


4 


3 


3 


CDMA Channels K 
for-~= 100 or 20 dB 


349 


326 


261 


239 


223 


203 


201 


CDMA Channels K 
for -tt=32 or 15 dB 


316 


292 


228 


206 


190 


170 


168 



Z=[(4-4) 2 - (X-Xf - 0'-V,) 2 ]2. 



(21) 



From equation (20) and (21), the user position (x, y, z) can be solved to obtain an initial 
approximation. The actual position must be solved iteratively or by utilizing a Kalman 
filter. From (x, y, z), the users altitude h, longitude and latitude can be derived. 



x = (R + h) cos 6 L cos 9[ 

y = {R + h) sin L cos 6 { 
z = {R + h) sin 0, 



(22) 
(23) 
(24) 



where L< d lt and h are solved by 



, cos 8 r 

-xan-Uz—^) 



(25) 
(26) 



(27) 



For a three satellite system, the position solution algorithm is much the same. The 
following equation substitutes for the fourth satellite equation 

X 2 + y 2 + z 2 = ( R + h ) 2 (28) 

As in the four satellite case, these four equations must be solved iteratively to obtain 
the users position. In the three satellite case, the user must report his altitude because 
only the longitude and latitude of his position can be determined from three satellites. 
The four non-linear equations are 

(</, - af = (* - x,-) 2 + (y-yf + z 2 /= 1, 2, 3 (29) 

x 2 +y 2 + z 2 = {R + h) 2 . (30) 

As in the four satellite case, the equation with index = 1 is subtracted from the 
other two equations. 

d x = a x x + B,j- + y\ (31) 

d x = o. 2 x + B 2 v + y 2 (32) 

where 



*3 ~ *1 



a 2 ' a 2 

2.2 2 2.2 

*1 + ■>'! ~ - Y 2 ~ }'2 + a 2 

2a 2 



(33) 



(34) 



(35) 



When we solve for y in terms of x, we get 

y = H x x + n 2 (36) 

where 

18 



y\ - V2 vi - 72 

B 3 — Bi ' B-) — Bi 



(37) 



The substitution of (36) into (31) produces 

d x = m 3 * + ^4 (38) 

where 

g I B 2 ~ ^2^1 Oigj ~ OgBj ,„. 

M3= B 2 -5, «•- Jfc-B, ' (39) 

The term z 2 can be expressed as 

z 2 = rf 2 - .r 2 -v 2 + lx x x + 2v,j- - x\ - y]. (40) 

Substitution of (36). (38). and (40) into (28) produces 

ax 2 + bx + c = (41) 

where 

a = nl (42) 

b = 2n 2 H4 + 2y lf i ] + 2x l (43) 

c = ix\ + 2y h u 2 - x 2 -y 1 - (R + h) 2 . (44) 

The value of x. y, and z can be calculated from (36), (40). and (41) subject to the 
limitation x < 6378 km provided the user knows what quadrant of the earth he is lo- 
cated in. 

E. POSITION ERROR 

Even though the satellite is geostationary, the satellite does move about its nominal 
position. The drift of the satellite can be calculated to less than 20 meters from its 
nominal position. The error that results in the user position determination can be cal- 
culated. The range error can be expressed as user position error (Ax, Ay, Az.) 



cd: dd, 6di 

M; = -rr-Ax + -r^-Ay + -r 1 - Az 
ex cy cz 

x-x t y-\) z- 

= — - — Ajc 4- — - — Av + — - 

d; d, " d; 



i= 1, 2, 3, 4. 



(45) 



-Az 



Equation (45) can be transformed into matrix form as Av = u and with equation (14), 

x ~ x \ y~ y'\ z — 2 



4 


4 


4 


x - x 2 


y- yj 


z-z 2 


d x -a 2 


d\-<h 


d\~a 2 


x - x 3 


y-y-3 


z~*3 


d x -a 3 


d x -a 3 


X - * 4 


y-y* 


z - z 4 



d] — « 4 d x — a 4 rfj — rt 4 



(46) 



(47) 



The user position error can then be simulated by letting the range error be 
Ad t = [(.v-*',.) 2 + 0-/,) 2 + (z-z'f'jT 



[(x-xf + (y-yf + (z-z,.) 2 ]2 



/= 1, 2, 3, 4 



where 



(.v',-, y h z'i) = (x t + Ax h }) + Ay h Zi + Az,). 



(48) 



(49) 



The variable Ad, is the difference between the distance from the user to the nominal 
satellite position and the distance from the user to the satellite position that the satellite 
may have drifted to. The variables (x'„ y'„ z',) are the coordinates of the nominal satellite 
position with the drift distances ( Ax„ Ay„ Az, ) added to the nominal satellite position 
coordinates. The error vector v is the linear least-squares solution of Av = u where 
v = {A T A)~ l A T u and the mean squared error is e = {Av — u) T (Av — u). The values 
(A.v, Ay, Az) are calculated using Eq. (46) and (47). The error contribution of the z co- 



ordinate is much less than the x or y coordinate as the user position approaches the 
equator. This ill-conditioned problem results in a poor estimation of Az which can be 
minimized by modifying the least-squares method of solution. By first calculating the 
least-squares estimate of Ax and Ay and ignoring the Az component of the total error 
and calculating Az after Ajc and Ay are found, a better estimate of the total error can be 
found. 



' A,)- A 



Az = {A 2 A 2 )~ l {A[u - A%A x v x ) 



(50) 
(51) 



where 



A, = 



4 




d\ 


x — x 2 


y 


— y 2 


d ] — a 2 


d\ 


~ a 7 


x - x 3 


y 
4 


~ }'3 


d \ - «3 


~ «3 


-V — X A 


y 


- J"4 



d\ ~ a A 



(52) 





d\ 




z 


- 


z 2 


dx 


~ 


a 2 


z 


- 


z 3 


4 


- 


«3 


z 


- 


^ 



(53) 



For a three satellite system, the range errors Ad, /= 1, 2, 3 are calculated from 
equation (45) and the user altitude error Ah is calculated from equation (30) as 



Ah 



x(Ax) + y(Ay) + z(Az) 

[x 2 + / + z 2 ]l 

x(Ax) + y(Ay) + z(Az) 

R + h 



(54) 



The user position error vector v = [Ax, Ay, Az~] T is the least-squares solution of 
Bv = w which is v = (B T £)-' B T w , where 



x - x ] y - y\ z - z ] 



d \ d \ d \ 

x ~ x 2 y - y 2 z - z 2 



d ] — a 2 d x — a 2 d^ — a 2 
x ~ x 2 y - y 3 z - z 3 



d \ ~ a 3 d\ ~ a 3 d \ ~ a 3 



(55) 



R + h R + h R + h 



Tor the three satellite case, the least-squares method is also modified to provide a better 
estimate of v. The variable v is calculated from v = [v,. Azl r where 



Az = (B[ B 2 )~ l (B[ w - B 2 T B ]V] ) 



(56) 
(57) 



and 



x - *i y - y\ 





d x 


dx 


X 


~ x 2 


y — >'2 


dx 


~ a i 


dx ~ "2 


X 


~ x 3 


y - >3 


dx 


- a 3 
X 


dx - «3 

y 



R + h R + h 





dx 




z 


- 


*2 


d\ 


- 


<*2 


z 


- 


z 3 


dx 


; 


«3 



R + h 



(58) 



Equations (50), (51), (56), and (57) calculate the upper limit of the error in the user 
position provided the satellites position errors are known in either the three of four sat- 
ellite case. The average error for various users positions has been compiled in [Ref. 1]. 
The average error in the users position increases as the user approaches the equator. 
The average error ranges from 14.2 to 61.5 meters depending on how close to the 
equator the user is. The closer the user is to the equator, the worse the error which in- 
dicates a weakness in the system. 

F. CONTROL STATION-TO-USER DATA LINK 
1. Uplink Bandwidth 

The frequency bandwidth allocated for the control station-to-satellite uplink is 
6524.5 to 6530.77 MHz. The 6.27 MHz bandwidth coincides with the available band- 
width of the satellite-to-user downlink part of the relay. 

After the control station has completed the calculations and the user position 
is determined, the position coordinates have to be sent to the user. A TDM channel is 
used to transport the user information to the user. To calculate the total carrier-to-noise 
density ratio of the control station-to-user link. Eqs. (5) - (8) are used as was discussed 
in the user-to-control link. 

The uplink frequency is 6533 MHz with an antenna gain (G,) of 44.5 dB. which 
is a standard antenna gain for a ground station antenna. The antenna gain is much 
higher than for a mobile vehicle as one is able to use a large dish. The power out (/>,) 
is set at only 1 watt per channnel since there would be more than one channel simul- 
taneously transmitted by the control station. For example, if 200 CDMA channels were 
used, then 200 watts of power would be required for transmission of the channels. The 
lower power out is standard for a ground station. For this link design, the satellite G T 
is -1.5 dB K. The power out and the satellite G,'T values are design parameters deter- 
mined by judgement and current systems. For the control station-to-user link, the total 
carrier-to-noise density ratio is 66.25 dB-Hz is calculated by Eq. (8). A carrier-to-noise 
density ratio of 66.25 dB-Hz is sufficient for a successful link. A 5 dB margin is engi- 
neered into the system to allow for the cross-interference degradation of the system by 
the multiple carriers that are transmitted by the control station. After subtracting the 
5 dB margin from the total carrier-to-noise density ratio, converting to a factor and di- 
viding the result by the required noise ratio factor, the data rate for the bit error proba- 
bilities of 10" 6 and 10-" are 42.2 kbps and 13.3 kbps, respectively. The calculations for 
the control station-to-user link utilize Eqs. (5) - (8), which have been discussed earlier. 



These are the same equations as Table 1 with only the input values differing. The con- 
trol station-to-user link analysis is tabulated in Table 6. 

Table 6. SYSTEM I CONTROL STATION-TO-USER LINK ANALYSIS 



Uplink Frequency 


6533 MHz 


Antenna Gain 


44.5 dB 


Transmitted Power 


1 W 


Carrier EIRP 


44.5 dBW 


Free Space Path Loss 


199 dB 


Satellite G/T 


-1.5 dB K 


Boltzmann's Constant 


-22S.6 dBW/K-Hz 


Uplink 

Carrier-to-Noise 

Density Ratio 


72.6 dB-Hz 


Downlink Frequency 


2491 MHz 


Satellite EIRP 


53.6 dBW 


Free Space Path Loss 


191 dB 


User G T 


-23. S dB K 


Downlink 
Carrier-to-Noise 

Density Ratio 


67.4dB-Ilz 


Total 

Carrier-to-Noise 

Density Ratio 


66.25 dB-Hz 


Margin 


5 dB 


If Required -rf- = 


15 dB 


20 dB 


Then Data Rate can be 


42.2 kbps 


13.3 kbps 



2. Control Station-to-User Data 

Using the available data bit rate, the user coordinates, identification tag and 
synchronization bits must be transmitted to each user that has requested a position fix. 
There are 58 bits required to represent the latitude, longitude, and altitude. Seven bits 
are allowed for degrees (where 2" =128 which will suffice to represent the users position 
if the user supplies to his machine the quadrant that he is in). There are 6 bits for min- 
utes, and 6 bits for seconds, where 2 6 = 64 will suffice to represent 60 values for both 



latitude and longitude. Another 20 bits are required to represent the user altitude. In 
Figure 3, a 40 bit code word is used for synchronization of the TDM frame. A 40 bit 
code word is a design parameter which is used in other communication systems. Each 
user information frame consists of two 8 bit flags, position information of 58 bits, gen- 
eral information of 20 bits and a user ID of 10 bits. The 8 bit flags provide the start and 
end of the user data. 



SYNC 


USER 1 


USER 2 




USER N 



1 














FLAG 


ID 


POSITION 
DATA 


GENERAL 
DATA 


FLAG 























Figure 4. TDM Frame (Control Station to Users) 



3. Satellite-to-User Downlink 

The data link from the control station to the user is completed with the 
satellite-to-user downlink at a frequency bandwidth of C.27 MHz between 2493.73 MHz 
and 2500 MHz. The satellite provides relay service only and does not process the data 
that is passed through. 



III. SYSTEM II 

A. SYSTEM II DESCRIPTION 

System II will employ 3 or 4 satellites in the same arrangement and positions as 
System I. System II differs from System I in the technique by which the differential 
distances are obtained. System II users will transmit a user unique pseudorandom 
ranging code to the control station via a satellite relay. The time delays between the ar- 
rivals of the codes from each of the satellites will determine the differential distances of 
the paths. Each time the user transmits a code, the code will travel to the satellites at 
the speed of light. The satellite that is closest will receive the code first and relay the 
code to the central control station. The closest satellite will provide the shortest time 
delay. The satellite that is furthest away from the user and the central control station 
will have the longest delay. It is these differences in the times of arrivals that determine 
the distance differentials as we did in System I. In System II, a total user-to-satellite and 
satellite-to-control station differential distance is calculated from the total time differen- 
tial. The centra] control station assumes the task of measuring the differences in the 
round trip distance between itself and the user via one satellite, arbitrarily designated as 
satellite one. and each of the other satellites. We define these differential distances as 

^■ = (/ 1 +^)-( / / + 4). i=l,2 f ...,/i (59) 

where / is the distance from the central control station to the satellite 

if = (x - xf + O-o -j,,.) 2 + (z - zf, / = 1, 2, ..., n (60) 

and d, is the distance from the user to the satellite 

dj = {x - xf + (y -yf + (z- zf, i- 1, 2, ..., n (61) 

For n = 4, Eqs. (9) - (11) combine to form a set of four independent equations and 
four unknowns, namely, x, y, z, and d x These four equations are 

(4 - *, + /, - if - (x - xf + (y-ytf + (z - zf, /= 1,2,3,4 (62) 

For n = 3. Eq. (4) is used in addition to Eq. (12) for /= 1, 2, 3 assuming the user 
altitude h is known. 



After the position solution is obtained, the control station relays the user position 
to the user via a satellite link as in System I. The frequency assignment and bandwidth 
allocated for each of the satellite links listed below are specified by the Federal Com- 
munications Commission in [Ref. 2]. 

• User-to-Control Station 

User-to-Satellite Uplink 
Frequency 1610 - 1626.5 MHz 
Bandwidth 16.5 MHz 
Satellite-to-Control Station Downlink 
Frequency 5150 - 5166.5 MHz 
Bandwidth 16.5 MHz 

• Control Station-to-User 

Control Station-to-Satellite Uplink 

Frequency 6524.5 - 6541 MHz 
Bandwidth 16.5 MHz 
Satellite-to- User Downlink 
Frequency 2483.5 - 2500 MHz 
Bandwidth 16.5 MHz 

• Control Station-to-Satellite Command Link 

Frequency 6526.5 - 6541.5 MHz 
Bandwidth 15 MHz 

B. USER-TO-CONTROL STATION LINK 

1. Uplink Bandwidth 

The frequency bandwidth allocated for the user-to-control station data link is 
16.5 MHz from 1610 MHz to 1626.5 MHz. Within this bandwidth, the user must 
transmit a PN ranging code, an identification code, general information, and user alti- 
tude in the three satellite configuration. The user will transmit a standard navigation 
1,023 chip Gold code sequence as the ranging code with the other data. The calculations 
for the user-to-control station are completed as was discussed in System I, utilizing Eqs. 
(5) - (8). System II design parameters are the same as System I. The total carrier-to- 
noise ratio less the 2 dB margin will support data rates of 57 kbps and 18 kbps for re- 
quired signal-to-noise ratios of 15 dB and 20 dB, respectively. The link analysis is 
tabulated in Table 7. 

2. User-to-Control Station Data 

As in System I. the user must transmit a 10 to 17 bit user identification number, 20 bits 
for additional information, and 20 bits for altitude if only three satellites are used. Using 
a standard modulation scheme, this information would be modulated by QPSK and 



Table 7. SYSTEM II USER-TO-CONTROL STATION LINK ANALYSIS 



Uplink Frequency 


1618 MHz 


Antenna Gain 


4dB 


Transmitted Power 


SOW 


Carrier EIRP 


23 dBW 


Free Space Path Loss 


190 dB 


Satellite G T 


+ 3 dB K 


Boltzmann's Constant 


-228.6 dBW K-Hz 


Uplink 
Carrier-to-Noise 

Density Ratio 


64.6 dB-Hz 


Downlink Frequency 


5150 MHz 


Satellite EIRP 


36 dBW 


Free Space Path Loss 


19S dB 


Control Station G/T 


20 dB K 


Downlink 

Carrier-to-Noise 

Density Ratio 


86.6 dB-Hz 


Total 

Carrier-to-Noise 

Density Ratio 


64.57 dB-Hz 


Margin 


2dB 


If Required -rr- = 


15 dB 


20 dB 


Then Data Rate can be 


57 kbps 


18 kbps 



spread with the 1023 chip Gold code. The number of CDMA channels that the system 
will support is the same as in System I. 

3. Satellite-to-Control Station Downlink 

The frequency bandwidth allocated for the satellite-to-control station downlink 
of the user-to-control station data link is 16.5 MHz from 5150 to 5165.5 MHz. The 
satellite functions as a relay onlv as in Svstem I. 



C. POSITION DETERMINATION 

The position of the user is determined in much the same manner as was done in the 
System I design. The main difference is that there are two distances that must be ac- 



counted for in the calculation. In System I, the satellites transmit the ranging code and 
the differential distances between the satellite and the user had to be accounted for in 
position error. In System II, the user transmits the code so the user-to-satellite and 
satellite-to-control station differential distances must be taken into consideration when 
calculating the users position. The differential distance measurements are made using 
Eq. (59). 

The central control station-to-satellite differential distance error does not contribute 
to the user position error as greatly as do the satellite-to-user distance differentials. The 
central control station would be suitably located away from the equator to minimize the 
control station-to-satellite differential distance measurement errors that are inherent to 
the system as was discussed in System I. In the three satellite configuration, where al- 
titude must be entered for position determination, the central control station knows its 
exact altitude, so the only altitude error entering into the position determination is from 
the user. In the four satellite configuration, satellite position errors between the user- 
to-satellite and central control station-to-satellite do increase the user position error but 
not as greatly as first thought. After conducting a computer simulation model run of 
1000 iterations with randomly varying satellite position errors between + 20 and - 20 
meters as was conducted m [Ref. I]; approximately a 1 to 2 meter additional error was 
added to the overall position error of System II in comparison with System I user posi- 
tion error. It was originally thought that a doubling of the position error would occur 
since an error in the satellite position affects both the user-to-satellite and the central 
control station-to-satellite paths, but was not the case. For this reason, the System II 
design is a viable alternative to System I design. 

D. CONTROL STATION-TO-USER DATA LINK 
1. Uplink Bandwidth 

The System II control station-to-user data link is designed the same as the data 
link in System I. The big advantage in System II is that the bandwidth allocated for the 
satellite-to-user downlink is used solely for the control station to user data link. The 
total bandwidth of 16.5 MHz can be utilized for data transmission because there is no 
ranging code to be transmitted by the satellites. In System I, the ranging code occupied 
10.23 MHz of the 16.5 MHz bandwidth allocated for the satellite to user link, leaving 
onlv 6.27 MHz for the control station-to-user data link. 



2. Control Station-to-User Data 

As in System I. the user ID, latitude, longitude, altitude and general information must 
be transmitted to the user. The System I TDM frame structure will also be utilized in 
System II. In System II, the number of users that can be serviced each second could 
be increased even further due to the 10.23 MHz increase in the available bandwidth. 
The increase in the number of users will depend on the protocols used and is beyond the 
scope of this thesis. The link calculations are completed using Eqs. (5) - (8) and System 
I link parameters. The values obtained in Table 8 are identical to those in System I for 
the same link parameters. Table 8 is furnished to present the fact that the link calcu- 
lations do not change. 

3. Satellite to User Downlink 

The satellite to user downlink occupies the full bandwidth of 16.5 MHz from 
1610 to 1626.5 MHz. The satellite operates as a passive relay only. 



Table 8. SYSTEM II CONTROL STATION-TO-USER LINK ANALYSIS 



Uplink Frequency 


6533 MHz 


Antenna Gain 


44.5 dB 


Transmitted Power 


1 W 


Carrier EI RP 


44.5 dBW 


Free Space Path Loss 


199 dB 


Satellite G T 


-1.5 dB K 


Boltzmann's Constant 


-228.6 dBW; K-Hz 


Uplink. 

Carrier-to-Noise 

Density Ratio 


72.6 dB-Hz 


Downlink Frequency 


2491 MHz 


Satellite EIRP 


53.6 dBW 


Free Space Path Loss 


191 dB 


UserG T 


-23.8 dB K 


Downlink 

Carrier-to-Noise 

Density Ratio 


66.25 dB-Hz 


Total 

Carrier-to-Noise 
Density Ratio 


61.73 dB-Hz 


Margin 


5dB 


If Required -77- = 


15 dB 


20 dB 


Then Data Rate can be 


42.2 kbps 


13.3 kbps 



IV. SYSTEM COMPARISONS AND CONCLUSIONS 

System II is the simpler system in many ways. A System II user sends the ranging 
code to the control station so the time of transmission does not require any synchroni- 
zation. The satellite does not require an on-board clock or a code generator and trans- 
ponder to send a ranging code to the user. There exists the possibility of using existing 
satellites or sharing future satellites. The user equipment is also simpler in that the user 
does not have to make time measurements of the satellite-to-user time differentials. By 
reducing the complexity of the user equipment, the cost to each user would also be re- 
duced. 

The number of users that could simultaneously be serviced by System II is also 
greater because the available bandwidth of the control station to user is dedicated totally 
to the link. In System I. the satellite-to-user bandwidth must also support the trans- 
mission of the ranging code from the satellite to the user reducing the bandwidth of the 
control station-to-user link. Although there is a slight increase in position error that is 
inherent to System II, the position accuracy is well within expected tolerances required 
of many civilian users. 

This thesis has proposed the concepts of two Global Satellite Location and Tracking 
Systems designed for the civilian user. The advantages of the systems are the low cost, 
user equipment simplicity, and accurate position determination. The user systems are 
cheaper because the computational hardware and software are maintained at the central 
control station. This eliminates the need for installing an expensive computer in each 
user transceiver. 

System II provides many possibilities for future design due to the fact that satellites 
already in space could be used as communications relays for the system. This eliminates 
the need to design and launch special satellites into space for location and tracking 
purposes only. 

Geostationary Satellite Location and Tracking Systems are viable systems for civil- 
ian position determination. 



V. LIST OF REFERENCES 

1. Ha, Tri T. and Robertson, R. Clark, Geostationary Satellite Navigation Systems, 
IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-23, NO. 2, 
Pages 247 - 254, March 1987. 

2. Manual of Regulations and Procedures for Federal Radio Frequency Management ; 3 
December 1985. 

3. Ha, Tri T., Digital Satellite Communications, McMillan Publishing Company, 1986. 

4. Spilker, James J. Jr., Digital Communications by Satellite, Prentice-Hall Inc., 1977. 

5. Shu Lin and J. Costello Jr., Error Control Coding: Fundamentals & Applications, 
Prentice-Hall, Inc., 1983. 

6. Thomas C. Bartee / Editor, Data Communications, Networks, and Systems, Howard 
W. Sams & Co.. 1985. 



VI. INITIAL DISTRIBUTION LIST 

No. Copies 

1. Defense Technical Information Center 2 
Cameron Station 

Alexandria, VA 22304-6145 

2. Library, Code 0142 2 
Naval Postgraduate School 

Monterey, CA 93943-5002 

3. Department Chairman. Code 62 1 
Department of Electrical and Computer Engineering 

Naval Postgraduate School 
Monterey, California 93943-5000 

4. Professor Tri T. Ha, Code 62Ha 5 
Department of Electrical and Computer Engineering 

Naval Postgraduate School 
Monterey, California 93943-5000 

5. Professor Glen A. Myers, Code 62Mv 2 
Department of Electrical and Computer Engineering 

Naval Postgraduate School 
Monterey. California 93943-5000 

6. Commander 1 

Naval Space Command 
ATTN: Code N3 
Dahlgren, Virginia 22448 

7. Commander 1 
United States Space Command 

ATTN: Technical Library 

Peterson Air Force Base, Colorado 80914 

8. Chief of Naval Operations 1 
ATTN: Naval Space Division (OP943) 

Washington, DC 20305-2000 

9. MR. Roger Casey 1 
Naval Ocean System Center 

ATTN: Code 805 

San Diego, California 92152-5000 

10. Major Danny L. DeFries 3 
ATTN: Science and Technology Center, EUROPE 

APO NY 09079 







n/ 




Thesis 






D2443 


DeFries 




c.l 


Inexpensive global lo- 
cation and tracking sys- 
tems using geostationary 
satellites. 



luesis 

D2443 

c.l 



DeFries 

Inexpensive global lo- 
cation and tracking sys- 
tems using geostationary 
satellites.